Question

2 1/3 + 3/7 divided by 2 1/3 x 1 3/7​

Answer 1

Answer: $\frac{29}{35}$

Step-by-step explanation:

1. Make sure all your denominators are the same, you can do this by multiplying them all by 3 or 7, 2 and 1/3 would become 2 7/21, 3/7 would become 9/21, 2 and 1/3, would become 2 and 7/21, and so on and so forth, leaving us with

2$\frac{7}{21}$+$\frac{9}{21}$ / 2$\frac{7}{21}$ * 1$\frac{9}{21}$

2. Now, I would go and solve each side of the equation because we divide them, we can add 2$\frac{7}{21}$ and $\frac{9}{21}$  together to get  2$\frac{16}{21}$, because 7 + 9 = 16

2$\frac{16}{21}$ / 2$\frac{7}{21}$ * 1$\frac{9}{21}$

3. We can do the same thing to the other side, by multiplying the two of them. I'm going to convert both of them to just fractions, 2$\frac{7}{21}$ becomes $\frac{49}{21}$ and 1$\frac{9}{21}$ becomes $\frac{30}{21}$

$\frac{49}{21}$ *  $\frac{30}{21}$

Now we can reduce them, and for our first fraction divide the top and bottom by 7, giving us  $\frac{7}{3}$ and the second one by 3, which gives us  $\frac{10}{7}$

$\frac{7}{3}$ * $\frac{10}{7}$ now we cross divide, where we replace the 7's with ones because they're right across from each other to get  $\frac{1}{3}$ and  $\frac{10}{1}$, or just 10.

$\frac{1}{3}$ * 10 =  $\frac{10}{3}$

4. So now we can do a similar thing with the first half of our equation and convert it into a fraction and not a mixed number.

$\frac{58}{21}$ / $\frac{10}{3}$

Now we multiply divide them, and the easiest way I learned how to do this was by keep the first fraction in its place, and flipping the denominator and numerator of the second, and multiplying them.

so   $\frac{58}{21}$ * $\frac{3}{10}$ which if we multiply both sides, you get $\frac{174}{210}$

I'll save you some times and simplify it for you, the greatest common factor is 6 so we divide the top and bottom by 6 to get

$\frac{29}{35}$